Information on Result #1019430
Linear OOA(12863, 699203, F128, 3, 18) (dual of [(699203, 3), 2097546, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12810, 150, F128, 3, 9) (dual of [(150, 3), 440, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,440P) [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- linear OOA(12853, 699053, F128, 3, 18) (dual of [(699053, 3), 2097106, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12853, 2097159, F128, 18) (dual of [2097159, 2097106, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(12853, 2097159, F128, 18) (dual of [2097159, 2097106, 19]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(12863, 233067, F128, 21, 18) (dual of [(233067, 21), 4894344, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |